Problem: Solve for $x$ and $y$ using elimination. ${-5x+2y = -22}$ ${-3x-2y = -42}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $-8x = -64$ $\dfrac{-8x}{{-8}} = \dfrac{-64}{{-8}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {-5x+2y = -22}\thinspace$ to find $y$ ${-5}{(8)}{ + 2y = -22}$ $-40+2y = -22$ $-40{+40} + 2y = -22{+40}$ $2y = 18$ $\dfrac{2y}{{2}} = \dfrac{18}{{2}}$ ${y = 9}$ You can also plug ${x = 8}$ into $\thinspace {-3x-2y = -42}\thinspace$ and get the same answer for $y$ : ${-3}{(8)}{ - 2y = -42}$ ${y = 9}$